A Nonlinear Transfer Technique for Renorming

• Κύριοι συγγραφείς: Moltó, Aníbal (Συγγραφέας), Orihuela, José (Συγγραφέας), Troyanski, Stanimir (Συγγραφέας), Valdivia, Manuel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2009.
• Σειρά: Lecture Notes in Mathematics, 1951
• Θέματα: Mathematics.; Functional analysis.; Differential geometry.; Differential Geometry.; Functional Analysis.

 Abstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem. Maps from a normed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering methods of metrization theory. Any one-to-one operator T from a reflexive space X into c0 (T) satisfies the authors' conditions, transferring the norm to X. Nevertheless the authors' maps can be far from linear, for instance the duality map from X to X* gives a non-linear example when the norm in X is Fréchet differentiable. This volume will be interesting for the broad spectrum of specialists working in Banach space theory, and for researchers in infinite dimensional functional analysis. 

 ?-Continuous and Co-?-continuous Maps -- Generalized Metric Spaces and Locally Uniformly Rotund Renormings -- ?-Slicely Continuous Maps -- Some Applications -- Some Open Problems.